Kappa Distributions: From Observational Evidences via Controversial Predictions to a Consistent Theory of Nonequilibrium Plasmas (Astrophysics and Space Science Library, 464)

This book presents recent results on the modelling of space plasmas with Kappa distributions and their interpretation. Hot and dilute space plasmas most often do not reach thermal equilibrium, their dynamics being essentially conditioned by the kinetic effects of plasma particles, i.e., electrons, protons, and heavier ions. Deviations from thermal equilibrium shown by these plasma particles are often described by Kappa distributions. Although well-known, these distributions are still controversial in achieving a statistical characterization and a physical interpretation of non-equilibrium plasmas. The results of the Kappa modelling presented here mark a significant progress with respect to all these aspects and open perspectives to understanding the high-resolution data collected by the new generation of telescopes and spacecraft missions. The book is directed to the large community of plasma astrophysics, including graduate students and specialists from associated disciplines, given the palette of the proposed topics reaching from applications to the solar atmosphere and the solar wind, via linear and quasilinear modelling of multi-species plasmas and waves within, to the fundamental physics of nonequilibrium plasmas. Contents Part I Introduction and Motivation 1 Introduction and Motivation 1.1 The Beginnings of Kappa Distributions 1.2 About Different Versions of Kappa Distributions 1.2.1 A Modified Kappa Distribution with κ-Independent Temperature 1.2.2 The Regularized Kappa Distribution 1.2.3 The Relativistic Kappa Distribution 1.3 Brief Outline of the Book References Part II New and Refined Observational Evidences of Kappa Distributions in Space Plasmas 2 Suprathermal Populations and Their Effects in Space Plasmas: Kappa vs. Maxwellian 2.1 Introduction: Empirical Kappa Models 2.2 Kappa-Distributed Electrons in the Solar Wind 2.2.1 Insights from Kappa Modeling 2.2.2 Properties of Halo Electrons 2.2.3 Properties of Strahl Electrons 2.3 Consequences of Kappa-Distributed Suprathermals 2.3.1 Atmospheres in Hydrostatic Equilibrium. Isotropic Kappa 2.3.2 The Influence of Altitude on Distributions and Macroscopic Properties 2.3.3 Anisotropic Distributions Above the Exobase 2.4 Conclusions References 3 Electron Kappa Distributions in the Solar Wind: Cause of the Acceleration or Consequence of the Expansion? 3.1 Introduction 3.2 Typical Examples of Solar Wind Electron Velocity Distribution Functions Observed at 1au 3.2.1 Non Maxwellian Core Electrons 3.3 Are the Electron Velocity Distributions Functions Maxwellians in the Solar Corona and Become Kappa-Like as the Wind Expands? 3.4 Are the Electron Velocity Distribution Functions Already Non-Maxwellians in the Solar Corona and Can We Measure This Property in-situ in the Solar Wind? References 4 Diagnostics of Kappa Distributions from Optically Thin Solar Spectra 4.1 Introduction 4.2 Calculations of Synthetic Spectra for Kappa Distributions 4.2.1 Line Intensities 4.2.2 Excitation Rates and the Relative Level Population 4.2.3 Ionization and Recombination Rates, Ionization Equilibrium 4.2.4 Sensitivity of Emission Lines to kappa 4.2.5 Continuum 4.3 Electron Kappa Distributions: Plasma Diagnostics from Line Intensities 4.3.1 Electron Density 4.3.2 Simultaneous Diagnostics of kappa and Temperature 4.3.3 Differential Emission Measures and Their Effects on Diagnostics 4.3.4 Transition Region Lines 4.4 Ion Kappa Distributions: Diagnostics from Line Profiles 4.4.1 Theory 4.4.2 Ion kappa-Distributions in Solar Flares 4.4.3 Ion kappa-Distributions in the Transition Region 4.4.4 Ion kappa-Distributions in the Solar Corona 4.5 Summary References 5 Non-thermal and Kappa Distributions in Solar Flare Radiative Signatures 5.1 Introduction to Non-thermal Electrons and Radiation in Flares 5.2 Theoretical Description of Kappa Distributions in Flares 5.3 Observational Evidence for Kappa Distributions in Flares 5.4 Kappa-Like Spectral Line Shapes in Solar Flares 5.4.1 The Production of Non-Gaussian Spectral Line Shapes 5.4.2 Observations of Non-Gaussian Spectral Line Shapes 5.5 Summary References Part III Physics Behind and Significance of Kappa Distributions in Plasma Astrophysics 6 Kappa Distribution Function: From Empirical to PhysicalConcepts 6.1 Why Kappa, and What Does This Model Bring New? 6.2 Kappa vs. Maxwellian Core 6.3 Prospects for Realistic Interpretations 6.3.1 Spontaneous Fluctuations and Suprathermal Populations 6.3.2 Suprathermals in Resonant Wave-Particle Interactions 6.4 Conclusions References 7 Kinetic Models of Wave-Electron Interaction in the Solar Corona and Wind 7.1 Kinetic Models 7.2 Resonant Wave-Electron Interaction 7.3 Kinetic Solar Wind Model with Whistler Waves 7.3.1 Interplanetary Whistler Wave Spectrum 7.3.2 The Simulation Setup 7.3.3 Kinetic Results for Solar Wind Electrons 7.4 Kappa-Like Tail Formation in the Solar Corona 7.4.1 Sufficient Wave Energy in the Corona? 7.4.2 The Model: Coronal Loop 7.4.3 Resulting Coronal Loop Electron VDFs References 8 On `Isobaric and Isentropic' Distribution Functions of Plasma Particles in the Heliosheath 8.1 Introduction 8.2 Families of Isobaric Kappa Distributions 8.3 The Relative Relativistic Pressure Reduction 8.4 A Direct Access to the Plasma Pressure 8.5 Isentropic Distribution Functions 8.6 Calculation of the Boltzmann Entropy of Isobaric Kappa Distributions 8.7 Entropic Calibration of a Non-equilibrium Distribution Functions 8.8 Conclusions References 9 Advanced Numerical Tools for Studying Waves and Instabilities in Kappa Distributed Plasmas 9.1 Introduction 9.2 Linear Dispersion for Drifting bi-Kappa Plasmas 9.3 Dispersion Solvers 9.4 Particle-in-Cell Simulations 9.5 Quasi-Linear Theory 9.6 Conclusions References 10 Advanced Interpretation of Waves and Instabilities in Space Plasmas 10.1 Introduction 10.2 Kinetic Theory of Space Plasmas: Linear and QL Approaches 10.3 Velocity Distribution Functions 10.4 Instabilities Driven by the bi-Kappa Distributed Electrons 10.4.1 Whistler Instability 10.4.2 Electron Mirror Instability 10.4.3 Electron Firehose Instabilities 10.5 Instabilities Driven by the bi-Kappa Distributed Ions 10.5.1 EM Ion Cyclotron Instability 10.5.2 Proton Mirror Instability 10.5.3 Proton Firehose Instability: Periodic Branch 10.6 Electromagnetic Instabilities of Electron Beams 10.6.1 Whistler Heat-flux Instability 10.6.2 Beaming Electron Firehose Instability 10.7 Electromagnetic Instabilities of Ion Beams 10.7.1 Ion–ion Resonant (EMIC-Beaming) Instability 10.7.2 Ion–ion Nonresonant Instability 10.7.3 Ion–ion RH Resonant Instability 10.8 Summary References Part IV Fundamental Aspects, Generalized Kappa Distributions, and Their Implications 11 Mathematical and Physical Characteristics of the Kappa Velocity Distribution 11.1 Introduction 11.2 Mathematical Aspects of Kappa Function 11.3 Possible Origin of Kappa Velocity Distribution 11.4 Physical Characteristics of Kappa Velocity Distribution 11.4.1 Harris Sheet Equilibrium in Nonthermal Plasmas 11.4.2 Electrostatic Solitary Waves in Nonthermal Plasmas 11.5 Mathematical and Physical Implications of Kappa Velocity Distribution 11.6 Summary References 12 Non-equilibrium Statistical Mechanics of Electron Kappa Distribution 12.1 Introduction 12.2 Scientific Background and Motivation 12.3 Overview of Non-Equilibrium Statistical Mechanics of Plasmas 12.3.1 General Formulation 12.3.2 Wave Kinetic Equation for Collective Eigenmodes 12.3.3 Particle Kinetic Equation 12.4 Plasma Turbulence and Non-Maxwellian Electron Distribution 12.4.1 Beam-Plasma Instability, Langmuir Turbulence, and Non-Thermal Electron Formation 12.4.2 Steady-State Langmuir Turbulence and Electron Kappa Distribution 12.5 Alternative Approach to Non-Thermal Distributions 12.5.1 Regularized (or Modified) Kappa Distribution 12.5.2 Dynamic Equilibrium Subject to Combined Collective and Collisional Processes 12.6 Conclusions References 13 Regularized Kappa Distributions: Linear Dispersion and Stability Theory 13.1 Introduction 13.2 From Standard to Regularized Kappa Distribution 13.3 Linear Dispersion Theory 13.4 Results 13.4.1 Damped Langmuir Modes 13.4.2 Damped Electromagnetic Cyclotron Modes 13.4.3 Electromagnetic Cyclotron Instabilities 13.4.4 Firehose Instabilities 13.5 Summary Appendix References 14 Kappa Distributions and Entropy 14.1 Introduction 14.2 The Gibbs Entropy 14.3 Application to Maxwellian and RKD Plasmas 14.4 Special Cases of the RKD Entropy 14.5 Quantitative Comparison of the RKD and the Maxwellian Entropy 14.6 Generalizations 14.7 Summary and Conclusion References 15 From Standard Kappa to a Regularized Kappa, or Even More Generalized Kappa ``Cookbook'' 15.1 Introduction and Fundamental Physics 15.2 The Generalized (Anisotropic) Kappa-Distribution 15.3 Properties of the GIK 15.4 The Debye Length and Superluminal Particles 15.5 An Application of the GIK 15.6 An Application of the GAK 15.7 Conclusions References Part V Concluding Remarks and Future Perspectives 16 Kappa Distributions: Concluding Remarks and Perspectives References Correction to: Electron Kappa Distributions in the Solar Wind: Cause of the Acceleration or Consequence of the Expansion? Index